Finite Group Databasebeta

← #11803599

Subgroups — #11803599

Order 1152.

1465 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic, complemented
2C2×#63909C211yesmaximal, characteristic
3C2×#63894C211yesmaximal, characteristic, complemented
4#10592638C211yesmaximal, characteristic, complemented
5C3×#4928C211yesmaximal, characteristic, complemented
6#10591384C212yesmaximal, complemented
7#10591374C212yesmaximal, complemented
8#10591313C211yesmaximal, characteristic, complemented
9#10591275C212yesmaximal, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591258C212yesmaximal, complemented
12#82236—31nomaximal
13#76198—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#626C2212yes—
17C22×#624C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2212yes—
20C2×#3752C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#872—24no—
31C2×#3722C2212yes—
32C2×#3722C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35#63909C418yescomplemented
36#63894—24no—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×#930—31no—
42C2×#895—31no—
43C2×#893—31no—
44C2×C4×D12—31no—
45C2×#872D311yescharacteristic, complemented
46C3×#389—31no—
47#5212—31no—
48#4990—32no—
49#4989—32no—
50#4989—32no—
51#4988—32no—
52#4987—31no—
53Dic3×C4⋊C4—31no—
54#4957—32no—
55#4956—32no—
56#4939—31no—
57#4939—31no—
58#4939—61no—
59C4×C4⋊Dic3—31no—
60#4928D311yescharacteristic, complemented
61#4669—32no—
62#4665—32no—
63C23×C3⋊D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)C2×C414yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3C2×C414yescomplemented
80C2×#626—42no—
81C2×#626—42no—
82C2×#626C2×C418yescomplemented
83C2×#624—24no—
84C2×#624—42no—
85C2×#624—42no—
86C32×C42—22no—
87#3752—42no—
88#3752—42no—
89C4⋊(C3⋊Dic3)—22no—
90C3×(C2×D3)⋊C4—22no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3C2×C414yescomplemented
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—42no—
97C3×C4×Dic3D414yescomplemented
98#3722—24no—
99#3722C2×C418yescomplemented
100(C2×D3)⋊Dic3—42no—
101Dic32—42no—
102#2324—91noSylow
103C23×C3×C4—31no—
104C22×#67—32no—
105C22×D12—31no—
106C22×D12—31no—
107C22×D12—32no—
108C22×D12—61no—
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C22×C4×D3C2×D311yescharacteristic
112C3×#117—64no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—32no—
118C2×C3×C22⋊C4—31no—
119C2×C3×C22⋊C4—31no—
120C2×C3×C42—21no—
121C2×C3×C42—31no—
122C2×C3×C42C2×D311yescharacteristic
123C2×C3×C42C2×D311yescharacteristic
124C2×#217—32no—
125#930—38no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—62no—
136C2×(C2×D3)⋊C4—62no—
137C2×(C2×D3)⋊C4C2×D311yescharacteristic
138C2×(C2×D3)⋊C4C2×D311yescharacteristic
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—61no—
142C2×C4⋊Dic3C2×D311yescharacteristic
143C2×C4⋊Dic3C2×D311yescharacteristic
144C2×Dic3⋊C4C2×D311yescharacteristic
145C2×Dic3⋊C4C2×D311yescharacteristic
146C2×Dic3⋊C4C2×D312yes—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3C2×D311yescharacteristic
150#895—38no—
151#893—64no—
152C4×D12—64no—
153#872—24no—
154C3×#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95C2×D312yes—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3C22×C414yes—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3—21no—
174C22×C3×D3C22×C412yes—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4C22×C412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4#4112yes—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C4⋊(C3⋊D3)—28no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3C22×C412yes—
200C2×C3×Dic3C22×C414yes—
201C2×C3×Dic3C2×D412yes—
202C2×C3×Dic3C2×D412yes—
203C3×C4×D3—28no—
204#626—48no—
205#624—48no—
206C2×#121—91no—
207C2×C4×D4—91no—
208C2×#117—31no—
209#390—92no—
210#390—91no—
211#389—31no—
212#388—92no—
213#386—92no—
214#385—92no—
215#380—91no—
216C4×C4⋊C4—91no—
217C24×C3—31no—
218C23×D3—32no—
219C23×D3—32no—
220C23×D3—62no—
221C23×D3C22×D311yescharacteristic
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—32no—
228C22×C3×C4—31no—
229C22×C3×C4—34no—
230C22×C3×C4—32no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—38no—
240C2×#67—122no—
241C2×#67—122no—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—62no—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D311yescharacteristic
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D311yescharacteristic
249C22×Dic3C22×D311yescharacteristic
250C2×D12—34no—
251C2×D12—34no—
252C2×D12—38no—
253C2×D12—64no—
254C2×D12—62no—
255C2×D12—62no—
256C2×D12—62no—
257C2×D12—62no—
258C2×D12—122no—
259C2×D12—122no—
260C2×D12—122no—
261C2×D12—122no—
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3—64no—
265C2×C4×D3—64no—
266C2×C4×D3—122no—
267C2×C4×D3—122no—
268C2×C4×D3—122no—
269C2×C4×D3—122no—
270C2×C4×D3C4×D314yescomplemented
271C3×C4⋊C4—34no—
272C3×C4⋊C4—62no—
273C3×C4⋊C4—62no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4—122no—
276C3×C22⋊C4—62no—
277C3×C22⋊C4—62no—
278C3×C42—22no—
279C3×C42—22no—
280C3×C42—34no—
281C3×C42—42no—
282#217—122no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—22no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4—38no—
287(C2×D3)⋊C4—64no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—122no—
290(C2×D3)⋊C4—122no—
291(C2×D3)⋊C4—122no—
292(C2×D3)⋊C4—122no—
293(C2×D3)⋊C4—122no—
294(C2×D3)⋊C4—124no—
295(C2×D3)⋊C4—124no—
296C4⋊Dic3—22no—
297C4⋊Dic3—62no—
298C4⋊Dic3—62no—
299C4⋊Dic3—122no—
300C4⋊Dic3C4×D314yescomplemented
301Dic3⋊C4—22no—
302Dic3⋊C4—22no—
303Dic3⋊C4—42no—
304C4×Dic3—122no—
305C4×Dic3—122no—
306C4×Dic3#6714yescomplemented
307C22×C32C23×C411yescharacteristic
308C22×C32C22×D411yescharacteristic
309C22×C32C2×#4111yescharacteristic
310C22×C32H(5,𝔽2)11yescharacteristic
311C22×C32H(5,𝔽2)11yescharacteristic
312C22×C32H(5,𝔽2)11yescharacteristic
313C22×C322−1+411yescharacteristic
314C2×C3⋊D3—24no—
315C2×C3⋊D3—24no—
316C2×C3⋊D3—24no—
317C2×C3⋊D3—42no—
318C2×C3⋊D3—42no—
319C2×C3⋊D3—42no—
320C2×C3⋊D3—42no—
321C2×C3×D3—22no—
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—41no—
329C32×C4—41no—
330C32×C4C4×D414yes—
331C3⋊Dic3—42no—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3—42no—
337C22×D4—92no—
338C22×D4—91no—
339C23×C4—31no—
340C23×C4—92no—
341#121—98no—
342C4×D4—184no—
343#117—64no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—32no—
349C2×C4⋊C4—91no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—31no—
352C2×C22⋊C4—92no—
353C2×C22⋊C4—92no—
354C2×C22⋊C4—92no—
355C2×C22⋊C4—92no—
356C2×C22⋊C4—92no—
357C2×C42—31no—
358C2×C42—92no—
359C2×C42D3211yescharacteristic
360#95—32no—
361#95—92no—
362#95—92no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—61no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3—61no—
369C23×C3—61no—
370C23×C3—61no—
371C23×C3C23×D311yescharacteristic
372C23×C3C23×D311yescharacteristic
373C22×D3—21no—
374C22×D3—21no—
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—34no—
380C22×D3—34no—
381C22×D3—64no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—62no—
387C22×D3—62no—
388C22×D3—62no—
389C22×D3—62no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—122no—
395C22×D3—122no—
396C22×D3—122no—
397C22×D3—122no—
398C22×D3—122no—
399C22×D3—122no—
400C22×D3C2×C4×D312yes—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—32no—
419C2×C3×C4—34no—
420C2×C3×C4—32no—
421C2×C3×C4—32no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—61no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—61no—
434C2×C3×C4—68no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—62no—
438C2×C3×C4C2×C4×D312yes—
439C2×C3×C4C2×C4×D312yes—
440C2×C3×C4#23512yes—
441C2×C3×C4D3×D412yes—
442C2×C3×C4#23912yes—
443C2×C3×C4C2×#6712yes—
444#67—128no—
445C2×Dic3—21no—
446C2×Dic3—22no—
447C2×Dic3—21no—
448C2×Dic3—22no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—62no—
462C2×Dic3—122no—
463C2×Dic3—122no—
464C2×Dic3—122no—
465C2×Dic3C2×C4×D314yes—
466C2×Dic3C2×C4×D312yes—
467C2×Dic3C2×#6712yes—
468C2×Dic3C2×#6712yes—
469D12—68no—
470D12—68no—
471D12—128no—
472D12—128no—
473C4×D3—28no—
474C4×D3—128no—
475C4×D3—128no—
476C2×C32C2×C4×D411yescharacteristic
477C2×C32#51811yescharacteristic
478C2×C32#52011yescharacteristic
479C2×C32#53511yescharacteristic
480C2×C32#53711yescharacteristic
481C2×C32#54011yescharacteristic
482C2×C32#54211yescharacteristic
483C3⋊D3—44no—
484C3×D3—42no—
485C24—31no—
486C24—92no—
487C2×D4—98no—
488C2×D4—94no—
489C2×D4—182no—
490C2×D4—182no—
491C2×D4—362no—
492C2×D4—362no—
493C22×C4—32no—
494C22×C4—31no—
495C22×C4—31no—
496C22×C4—31no—
497C22×C4—34no—
498C22×C4—32no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—92no—
502C22×C4—184no—
503C22×C4—362no—
504C22×C4—362no—
505C22×C4C2×D3211yescharacteristic
506C22×C4C2×D3211yescharacteristic
507C22×C4C2×D3211yescharacteristic
508C4⋊C4—34no—
509C4⋊C4—62no—
510C4⋊C4—62no—
511C4⋊C4—62no—
512C4⋊C4—122no—
513C4⋊C4—182no—
514C22⋊C4—62no—
515C22⋊C4—62no—
516C22⋊C4—98no—
517C22⋊C4—184no—
518C22⋊C4—362no—
519C22⋊C4—362no—
520C22⋊C4—362no—
521C42—22no—
522C42—34no—
523C42—362no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—62no—
532C22×C3—62no—
533C22×C3—62no—
534C22×C3—121no—
535C22×C3—121no—
536C22×C3—121no—
537C22×C3—121no—
538C22×C3C22×C4×D311yescharacteristic
539C22×C3C22×C4×D311yescharacteristic
540C22×C3C2×#23511yescharacteristic
541C22×C3C2×D3×D411yescharacteristic
542C22×C3#100411yescharacteristic
543C22×C3C2×#23911yescharacteristic
544C22×C3#100711yescharacteristic
545C22×C3#100911yescharacteristic
546C22×C3#100911yescharacteristic
547C22×C3#100911yescharacteristic
548C22×C3#100911yescharacteristic
549C22×C3#100911yescharacteristic
550C22×C3#101011yescharacteristic
551C22×C3C22×#6711yescharacteristic
552C2×D3—22no—
553C2×D3—22no—
554C2×D3—22no—
555C2×D3—41no—
556C2×D3—41no—
557C2×D3—41no—
558C2×D3—41no—
559C2×D3—64no—
560C2×D3—64no—
561C2×D3—64no—
562C2×D3—64no—
563C2×D3—64no—
564C2×D3—64no—
565C2×D3—124no—
566C2×D3—124no—
567C2×D3—124no—
568C2×D3—122no—
569C2×D3—122no—
570C2×D3—122no—
571C2×D3—122no—
572C2×D3—122no—
573C2×D3—122no—
574C2×D3—122no—
575C2×D3—122no—
576C2×D3—242no—
577C2×D3—242no—
578C2×D3—242no—
579C2×D3—242no—
580C3×C4—24no—
581C3×C4—42no—
582C3×C4—42no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—62no—
588C3×C4—64no—
589C3×C4—62no—
590C3×C4—62no—
591C3×C4—122no—
592C3×C4#89314yes—
593C3×C4C4×#6714yes—
594Dic3—22no—
595Dic3—24no—
596Dic3—22no—
597Dic3—22no—
598Dic3—42no—
599Dic3—122no—
600Dic3—122no—
601Dic3—242no—
602C32#232411yescharacteristic, complemented, Sylow
603C23—32no—
604C23—61no—
605C23—61no—
606C23—61no—
607C23—61no—
608C23—61no—
609C23—61no—
610C23—94no—
611C23—182no—
612C23—182no—
613C23—182no—
614C23—182no—
615C23—182no—
616C23—182no—
617C23C22×D3211yescharacteristic
618D4—188no—
619D4—368no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—32no—
627C2×C4—34no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—62no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—62no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—68no—
639C2×C4—62no—
640C2×C4—62no—
641C2×C4—62no—
642C2×C4—182no—
643C2×C4—182no—
644C2×C4—182no—
645C2×C4—368no—
646C2×C4#379912yes—
647C2×C4C4×D3212yes—
648C2×C4D3×#6712yes—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—122no—
657C2×C3C2×#89311yescharacteristic
658C2×C3#552111yescharacteristic
659C2×C3#552311yescharacteristic
660C2×C3#553411yescharacteristic
661C2×C3#553511yescharacteristic
662C2×C3#554511yescharacteristic
663C2×C3#557411yescharacteristic
664C2×C3#560711yescharacteristic
665C2×C3#562911yescharacteristic
666C2×C3#569711yescharacteristic
667C2×C3#573311yescharacteristic
668C2×C3C2×C4×#6711yescharacteristic
669C2×C3#583011yescharacteristic
670C2×C3#583311yescharacteristic
671D3—42no—
672D3—124no—
673D3—124no—
674D3—244no—
675C22—62no—
676C22—62no—
677C22—62no—
678C22—121no—
679C22—121no—
680C22—121no—
681C22—121no—
682C22—184no—
683C22—184no—
684C22—184no—
685C22—362no—
686C22—362no—
687C22—362no—
688C22—362no—
689C22#6429711yescharacteristic
690C22C2×#379911yescharacteristic
691C22C2×C4×D3211yescharacteristic
692C22#6430711yescharacteristic
693C22#6430811yescharacteristic
694C22#6430811yescharacteristic
695C22C2×D3×#6711yescharacteristic
696C4—41no—
697C4—41no—
698C4—62no—
699C4—62no—
700C4—64no—
701C4—62no—
702C4—122no—
703C4—362no—
704C4#6390414yes—
705C3—21no—
706C3#7619811yescharacteristic, complemented
707C3#8223611yescharacteristic, complemented
708C2—122no—
709C2—364no—
710C2#1059387711yescharacteristic
711C2#1059389011yescharacteristic
712C2#1059398911yescharacteristic
713C2#1059399411yescharacteristic
714C2#1059489411yescharacteristic
715C2C2×#6390411yescharacteristic
716C2#1059506411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63909C2
hypercenterC2×C42D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#872C2semidirect
3. C2×#63894C2semidirect
4. #10592638C2semidirect
5. C3×#4928C2semidirect
6. #10591384C2semidirect
7. #10591374C2semidirect
8. #10591313C2semidirect
9. #10591275C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591258C2semidirect
35. #63909C4semidirect
45. C2×#872D3semidirect
60. #4928D3semidirect
79. C2×C3×C4×D3C2×C4semidirect
82. C2×#626C2×C4semidirect
93. C3×C4⋊Dic3C2×C4semidirect
97. C3×C4×Dic3D4semidirect
99. #3722C2×C4semidirect
270. C2×C4×D3C4×D3semidirect
300. C4⋊Dic3C4×D3semidirect
306. C4×Dic3#67semidirect
602. C32#2324semidirect
706. C3#76198semidirect
707. C3#82236semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#8722
C2×#639092
C2×#638942
#105926382
C3×#49282
#105913842
#105913742
#105913132
#105912752
Dic3×C4⋊Dic32
#105912582
#822363
#761983